FLINT: Coupling Proximal Initialization and Bounded Stochasticity for Flow-Matching Inverse Problems

Junseo Bang, Daewon Choi, Dong Ju Mun, Se Young Chun

Flow matching models have emerged as a dominant paradigm for generative posterior sampling in imaging inverse problems. Existing solvers follow two distinct lines of work: trajectory-space methods, which refine sampling dynamics from random initial noise, and source-space methods, which optimize the initial noise itself. While most prior work treats these as independent design choices, we show that they are inherently coupled. We derive a unified stability bound that links initialization proximity and cumulative sampling stochasticity through a multiplicative envelope, complemented by two empirical observations. First, we identify a sufficiency regime in which a moderately optimized proximal source initialization is enough to attain the performance plateau, rendering exhaustive source-space optimization unnecessary. Second, this initial advantage is fragile: it is eroded by excessive stochasticity accumulation during guided sampling, necessitating a mechanism that bounds the cumulative noise injection. These findings motivate FLINT, a two-stage framework that operationalizes this coupling. FLINT establishes a high-fidelity starting point via a manifold-constrained proximal…